Pressure

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Pressure

 

Pressure exerted by particle collisions inside a closed container. The collisions that exert the pressure are highlighted in red.
Common symbols	p, P
SI unit	pascal (Pa)
In SI base units	kg⋅m−1⋅s−2
Derivations from other quantities	p = F / A
Dimension	${\displaystyle \mathsf{M}{\mathsf{L}}^{-1}{\mathsf{T}}^{-2}}$

Thermodynamics
The classical Carnot heat engine

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled gage pressure) is the pressure relative to the ambient pressure.

Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m²); similarly, the pound-force per square inch (psi, symbol lbf/in²) is the traditional unit of pressure in the imperial and US customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the unit atmosphere (atm) is equal to this pressure, and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Definition

Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is "p" or P. The IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.

Formula

Conjugate variables of thermodynamics

Pressure Volume (Stress) (Strain) Temperature Entropy Chemical potential Particle number

Mathematically: $${\displaystyle p=\frac{F}{A},\text{ or }P=\frac{F}{A},}$$ where:

• ${\displaystyle p}$ is the pressure,
• ${\displaystyle F}$ is the magnitude of the normal force,
• ${\displaystyle A}$ is the area of the surface on contact.

Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates these two normal vectors: $${\displaystyle d{\mathbf{F}}_n=-pd\mathbf{A}=-p\mathbf{n}dA.}$$

The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.

It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.

Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume. It is defined as a derivative of the internal energy of a system:

$${\displaystyle p=-{\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }V}\right)}_{S,N},}$$

where:

• ${\displaystyle U}$ is the internal energy,
• ${\displaystyle V}$ is the volume of the system,
• The subscripts mean that the derivative is taken at fixed entropy (${\displaystyle S}$) and particle number (${\displaystyle N}$).

Units

Mercury column

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m², or kg·m⁻¹·s⁻²). This name for the unit was added in 1971; before that, pressure in SI was expressed in newtons per square metre.

Other units of pressure, such as pounds per square inch (lbf/in²) and bar, are also in common use. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm⁻², or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre ("g/cm²" or "kg/cm²") and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is deprecated in SI. The technical atmosphere (symbol: at) is 1 kgf/cm² (98.0665 kPa, or 14.223 psi).

Pressure is related to energy density and may be expressed in units such as joules per cubic metre (J/m³, which is equal to Pa). Mathematically: $${\displaystyle p=\frac{F\cdot \text{distance}}{A\cdot \text{distance}}=\frac{\text{work}}{\text{volume}}=\frac{\text{energy (J)}}{\text{volume }({\text{m}}^3)}.}$$

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.

The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa (IUPAC recommends the value 100000 Pa, but prior to 1982 the value 101325 Pa (= 1 atm) was usually used).

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely.

When millimetres of mercury (or inches of mercury) are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres (or centimetres) of mercury in most of the world, and lung pressures in centimetres of water are still common.

Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar (= 10,000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm (1 atm = 101,325 Pa / 33.066 = 3,064.326 Pa). The pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.

Gauge pressure is often given in units with "g" appended, e.g. "kPag", "barg" or "psig", and units for measurements of absolute pressure are sometimes given a suffix of "a", to avoid confusion, for example "kPaa", "psia". However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure. For example, "p_g = 100 psi" rather than "p = 100 psig".

Differential pressure is expressed in units with "d" appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.

Presently or formerly popular pressure units include the following:

• atmosphere (atm)
• manometric units:
  • centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
  • height of equivalent column of water, including millimetre (mm H
    ₂O), centimetre (cm H
    ₂O), metre, inch, and foot of water;
• imperial and customary units:
  • kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch,
  • short ton-force and long ton-force per square inch,
  • fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression;
• non-SI metric units:
  • bar, decibar, millibar,
    • msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression,
  • kilogram-force, or kilopond, per square centimetre (technical atmosphere),
  • gram-force and tonne-force (metric ton-force) per square centimetre,
  • barye (dyne per square centimetre),
  • kilogram-force and tonne-force per square metre,
  • sthene per square metre (pieze).

Examples

The effects of an external pressure of 700 bar on an aluminum cylinder with 5 mm (0.197 in) wall thickness

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density.

Another example is a knife. If the flat edge is used, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressure.

For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa (32 psi)", but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi), the absolute pressure in the tire is therefore about 320 kPa (46 psi). In technical work, this is written "a gauge pressure of 220 kPa (32 psi)".

Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)", is permitted. In non-SI technical work, a gauge pressure of 32 psi (220 kPa) is sometimes written as "32 psig", and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa (15 psi), a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.^{[citation needed]}

Scalar nature

In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because there are an extremely large number of molecules and because the motion of the individual molecules is random in every direction, no motion is detected. When the gas is at least partially confined (that is, not free to expand rapidly), the gas will exhibit a hydrostatic pressure. This confinement can be achieved with either a physical container, or in the gravitational well of a large mass, such as a planet, otherwise known as atmospheric pressure.

In the case of planetary atmospheres, the pressure-gradient force of the gas pushing outwards from higher pressure, lower altitudes to lower pressure, higher altitudes is balanced by the gravitational force, preventing the gas from diffusing into outer space and maintaining hydrostatic equilibrium.

In a physical container, the pressure of the gas originates from the molecules colliding with the walls of the container. The walls of the container can be anywhere inside the gas, and the force per unit area (the pressure) is the same. If the "container" is shrunk down to a very small point (becoming less true as the atomic scale is approached), the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.

A closely related quantity is the stress tensor σ, which relates the vector force ${\displaystyle \mathbf{F}}$ to the vector area ${\displaystyle \mathbf{A}}$ via the linear relation ${\displaystyle \mathbf{F}=\sigma \mathbf{A}}$.

This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.

According to the theory of general relativity, pressure increases the strength of a gravitational field (see stress–energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at everyday pressures but is significant in neutron stars, although it has not been experimentally tested.

Types

Fluid pressure

Fluid pressure is most often the compressive stress at some point within a fluid. (The term fluid refers to both liquids and gases – for more information specifically about liquid pressure, see section below.)

Water escapes at high speed from a damaged hydrant that contains water at high pressure (due to high pressure of the water it behaves like it is sprayed)

Fluid pressure occurs in one of two situations:

• An open condition, called "open channel flow", e.g. the ocean, a swimming pool, or the atmosphere.
• A closed condition, called "closed conduit", e.g. a water line or gas line.

Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.

Closed bodies of fluid are either "static", when the fluid is not moving, or "dynamic", when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.

The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. Bernoulli's equation can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal and incompressible. An ideal fluid is a fluid in which there is no friction, it is inviscid (zero viscosity). The equation for all points of a system filled with a constant-density fluid is $${\displaystyle \frac{p}{\gamma }+\frac{v^2}{2g}+z=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t},}$$

where:

• p, pressure of the fluid,
• ${\displaystyle \gamma }$ = ρg, density × acceleration of gravity is the (volume-) specific weight of the fluid,
• v, velocity of the fluid,
• g, acceleration of gravity,
• z, elevation,
• ${\displaystyle \frac{p}{\gamma }}$, pressure head,
• ${\displaystyle \frac{v^2}{2g}}$, velocity head.

Applications

• Hydraulic brakes
• Artesian well
• Blood pressure
• Hydraulic head
• Plant cell turgidity
• Pythagorean cup
• Pressure washing

Explosion or deflagration pressures

Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures

Low-pressure chamber in Bundesleistungszentrum Kienbaum, Germany

While pressures are, in general, positive, there are several situations in which negative pressures may be encountered:

• When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa). For example, abdominal decompression is an obstetric procedure during which negative gauge pressure is applied intermittently to a pregnant woman's abdomen.
• Negative absolute pressures are possible. They are effectively tension, and both bulk solids and bulk liquids can be put under negative absolute pressure by pulling on them. Microscopically, the molecules in solids and liquids have attractive interactions that overpower the thermal kinetic energy, so some tension can be sustained. Thermodynamically, however, a bulk material under negative pressure is in a metastable state, and it is especially fragile in the case of liquids where the negative pressure state is similar to superheating and is easily susceptible to cavitation. In certain situations, the cavitation can be avoided and negative pressures sustained indefinitely, for example, liquid mercury has been observed to sustain up to −425 atm in clean glass containers. Negative liquid pressures are thought to be involved in the ascent of sap in plants taller than 10 m (the atmospheric pressure head of water).
• The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed "vacuum pressure" (not to be confused with the negative gauge pressure of a vacuum).
• For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive stress along one surface normal, with a component of negative stress acting along another surface normal. The pressure is then defined as the average of the three principal stresses.
  • The stresses in an electromagnetic field are generally non-isotropic, with the stress normal to one surface element (the normal stress) being negative, and positive for surface elements perpendicular to this.
• In cosmology, dark energy creates a very small yet cosmically significant amount of negative pressure, which accelerates the expansion of the universe.

Stagnation pressure

Main article: Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by: $${\displaystyle p_0=\frac{1}{2}\rho v^2+p}$$ where

• ${\displaystyle p_0}$ is the stagnation pressure,
• ${\displaystyle \rho }$ is the density,
• ${\displaystyle v}$ is the flow velocity,
• ${\displaystyle p}$ is the static pressure.

The pressure of a moving fluid can be measured using a Pitot tube, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures.

Surface pressure and surface tension

There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.

Surface pressure is denoted by π: $${\displaystyle \pi =\frac{F}{l}}$$ and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of Boyle's law, πA = k, at constant temperature.

Surface tension is another example of surface pressure, but with a reversed sign, because "tension" is the opposite to "pressure".

Pressure of an ideal gas

Main article: Ideal gas law

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume: $${\displaystyle p=\frac{nRT}{V},}$$ where:

• p is the absolute pressure of the gas,
• n is the amount of substance,
• T is the absolute temperature,
• V is the volume,
• R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.

Vapour pressure

Main article: Vapour pressure

Vapour pressure is the pressure of a vapour in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.

The atmospheric pressure boiling point of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapour bubbles inside the bulk of the substance. Bubble formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial vapor pressure.

Liquid pressure

See also: Fluid statics § Pressure in fluids at rest

When a person swims under the water, water pressure is felt acting on the person's eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.

Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. Thus, we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density and gravity at a depth within a substance is represented by the following formula: $${\displaystyle p=\rho gh,}$$ where:

• p is liquid pressure,
• g is gravity at the surface of overlaying material,
• ρ is density of liquid,
• h is height of liquid column or depth within a substance.

Another way of saying the same formula is the following: $${\displaystyle p=\text{weight}\times \text{density}\times \text{depth}.}$$

Derivation of this equation

The pressure a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.

Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.

The pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether their head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake.

If four interconnected vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference which vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the neighboring vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.

Restating this as an energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface of a stationary liquid in a vessel gravitational potential energy is large but liquid pressure is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure. The two energy components change linearly with the depth so the sum of pressure and gravitational potential energy per unit volume is constant throughout the volume of the fluid. The units of pressure are equivalent to energy per unit volume. (In the SI system of units, the pascal is equivalent to the joule per cubic metre.) Mathematically, it is described by Bernoulli's equation, where velocity head is zero and comparisons per unit volume in the vessel are $${\displaystyle \frac{p}{\gamma }+z=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}.}$$

Terms have the same meaning as in section Fluid pressure.

Direction of liquid pressure

An experimentally determined fact about liquid pressure is that it is exerted equally in all directions. If someone is submerged in water, no matter which way that person tilts their head, the person will feel the same amount of water pressure on their ears. Because a liquid can flow, this pressure is not only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a ball is pushed upward by water pressure (buoyancy).

When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure does not have a specific direction, force does. A submerged triangular block has water forced against each point from many directions, but components of the force that are not perpendicular to the surface cancel each other out, leaving only a net perpendicular point. This is why liquid particles' velocity only alters in a normal component after they are collided to the container's wall. Likewise, if the collision site is a hole, water spurting from the hole in a bucket initially exits the bucket in a direction at right angles to the surface of the bucket in which the hole is located. Then it curves downward due to gravity. If there are three holes in a bucket (top, bottom, and middle), then the force vectors perpendicular to the inner container surface will increase with increasing depth – that is, a greater pressure at the bottom makes it so that the bottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth surface is always at right angles to the surface. The speed of liquid out of the hole is ${\displaystyle \sqrt{2gh}}$, where h is the depth below the free surface.^[25] As predicted by Torricelli's law this is the same speed the water (or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure

$${\displaystyle P=\frac{p}{{\rho }_0}}$$ is the kinematic pressure, where ${\displaystyle p}$ is the pressure and ${\displaystyle {\rho }_0}$ constant mass density. The SI unit of P is m²/s². Kinematic pressure is used in the same manner as kinematic viscosity ${\displaystyle \nu }$ in order to compute the Navier–Stokes equation without explicitly showing the density ${\displaystyle {\rho }_0}$.

Navier–Stokes equation with kinematic quantities

$${\displaystyle \frac{\mathrm{\partial }u}{\mathrm{\partial }t}+(u\mathrm{\nabla })u=-\mathrm{\nabla }P+\nu {\mathrm{\nabla }}^{2}u.}$$

Vacuum

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Vacuum

Vacuum pump and bell jar for vacuum experiments, used in science education during the early 20th century, on display in the Schulhistorische Sammlung ('School Historical Museum'), Bremerhaven, Germany

A vacuum (pl.: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective vacuus (neuter vacuum) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure. The Latin term in vacuo is used to describe an object that is surrounded by a vacuum.

The quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. But higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth (10⁻¹²) of atmospheric pressure (100 nPa), and can reach around 100 particles/cm³. Outer space is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average in intergalactic space.

Vacuum has been a frequent topic of philosophical debate since ancient Greek times, but was not studied empirically until the 17th century. Clemens Timpler (1605) philosophized about the experimental possibility of producing a vacuum in small tubes. Evangelista Torricelli produced the first laboratory vacuum in 1643, and other experimental techniques were developed as a result of his theories of atmospheric pressure. A Torricellian vacuum is created by filling with mercury a tall glass container closed at one end, and then inverting it in a bowl to contain the mercury (see below).

Vacuum became a valuable industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes, and a wide array of vacuum technologies has since become available. The development of human spaceflight has raised interest in the impact of vacuum on human health, and on life forms in general.

Etymology

The word vacuum comes from Latin 'an empty space, void', noun use of neuter of vacuus, meaning "empty", related to vacare, meaning "to be empty".

Vacuum is one of the few words in the English language that contains two consecutive instances of the vowel u.

Historical understanding

Historically, there has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers debated the existence of a vacuum, or void, in the context of atomism, which posited void and atom as the fundamental explanatory elements of physics. Lucretius argued for the existence of vacuum in the first century BC and Hero of Alexandria tried unsuccessfully to create an artificial vacuum in the first century AD.

Following Plato, however, even the abstract concept of a featureless void faced considerable skepticism: it could not be apprehended by the senses, it could not, itself, provide additional explanatory power beyond the physical volume with which it was commensurate and, by definition, it was quite literally nothing at all, which cannot rightly be said to exist. Aristotle believed that no void could occur naturally, because the denser surrounding material continuum would immediately fill any incipient rarity that might give rise to a void. In his Physics, book IV, Aristotle offered numerous arguments against the void: for example, that motion through a medium which offered no impediment could continue ad infinitum, there being no reason that something would come to rest anywhere in particular.

In the medieval Muslim world, the physicist and Islamic scholar Al-Farabi wrote a treatise rejecting the existence of the vacuum in the 10th century. He concluded that air's volume can expand to fill available space, and therefore the concept of a perfect vacuum was incoherent. According to Ahmad Dallal, Abū Rayhān al-Bīrūnī states that "there is no observable evidence that rules out the possibility of vacuum". The suction pump was described by Arab engineer Al-Jazari in the 13th century, and later appeared in Europe from the 15th century.

European scholars such as Roger Bacon, Blasius of Parma and Walter Burley in the 13th and 14th century focused considerable attention on issues concerning the concept of a vacuum. The commonly held view that nature abhorred a vacuum was called horror vacui. There was even speculation that even God could not create a vacuum if he wanted and the 1277 Paris condemnations of Bishop Étienne Tempier, which required there to be no restrictions on the powers of God, led to the conclusion that God could create a vacuum if he so wished. From the 14th century onward increasingly departed from the Aristotelian perspective, scholars widely acknowledged that a supernatural void exists beyond the confines of the cosmos itself by the 17th century. This idea, influenced by Stoic physics, helped to segregate natural and theological concerns.

Almost two thousand years after Plato, René Descartes also proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy of void and atom. Although Descartes agreed with the contemporary position, that a vacuum does not occur in nature, the success of his namesake coordinate system and more implicitly, the spatial–corporeal component of his metaphysics would come to define the philosophically modern notion of empty space as a quantified extension of volume. By the ancient definition however, directional information and magnitude were conceptually distinct.

Torricelli's mercury barometer produced one of the first sustained vacuums in a laboratory.

Medieval thought experiments into the idea of a vacuum considered whether a vacuum was present, if only for an instant, between two flat plates when they were rapidly separated. There was much discussion of whether the air moved in quickly enough as the plates were separated, or, as Walter Burley postulated, whether a 'celestial agent' prevented the vacuum arising. Jean Buridan reported in the 14th century that teams of ten horses could not pull open bellows when the port was sealed.

The Crookes tube, used to discover and study cathode rays, was an evolution of the Geissler tube.

The 17th century saw the first attempts to quantify measurements of partial vacuum. Evangelista Torricelli's mercury barometer of 1643 and Blaise Pascal's experiments both demonstrated a partial vacuum.

In 1654, Otto von Guericke invented the first vacuum pump and conducted his famous Magdeburg hemispheres experiment, showing that, owing to atmospheric pressure outside the hemispheres, teams of horses could not separate two hemispheres from which the air had been partially evacuated. Robert Boyle improved Guericke's design and with the help of Robert Hooke further developed vacuum pump technology. Thereafter, research into the partial vacuum lapsed until 1850 when August Toepler invented the Toepler pump and in 1855 when Heinrich Geissler invented the mercury displacement pump, achieving a partial vacuum of about 10 Pa (0.1 Torr). A number of electrical properties become observable at this vacuum level, which renewed interest in further research.

While outer space provides the most rarefied example of a naturally occurring partial vacuum, the heavens were originally thought to be seamlessly filled by a rigid indestructible material called aether. Borrowing somewhat from the pneuma of Stoic physics, aether came to be regarded as the rarefied air from which it took its name, (see Aether (mythology)). Early theories of light posited a ubiquitous terrestrial and celestial medium through which light propagated. Additionally, the concept informed Isaac Newton's explanations of both refraction and of radiant heat. 19th century experiments into this luminiferous aether attempted to detect a minute drag on the Earth's orbit. While the Earth does, in fact, move through a relatively dense medium in comparison to that of interstellar space, the drag is so minuscule that it could not be detected. In 1912, astronomer Henry Pickering commented: "While the interstellar absorbing medium may be simply the ether, [it] is characteristic of a gas, and free gaseous molecules are certainly there". Thereafter, however, luminiferous aether was discarded.

Later, in 1930, Paul Dirac proposed a model of the vacuum as an infinite sea of particles possessing negative energy, called the Dirac sea. This theory helped refine the predictions of his earlier formulated Dirac equation, and successfully predicted the existence of the positron, confirmed two years later. Werner Heisenberg's uncertainty principle, formulated in 1927, predicted a fundamental limit within which instantaneous position and momentum, or energy and time can be measured. This far reaching consequences also threatened whether the "emptiness" of space between particles exists.

Classical field theories

The strictest criterion to define a vacuum is a region of space and time where all the components of the stress–energy tensor are zero. This means that this region is devoid of energy and momentum, and by consequence, it must be empty of particles and other physical fields (such as electromagnetism) that contain energy and momentum.

Gravity

In general relativity, a vanishing stress–energy tensor implies, through Einstein field equations, the vanishing of all the components of the Ricci tensor. Vacuum does not mean that the curvature of space-time is necessarily flat: the gravitational field can still produce curvature in a vacuum in the form of tidal forces and gravitational waves (technically, these phenomena are the components of the Weyl tensor). The black hole (with zero electric charge) is an elegant example of a region completely "filled" with vacuum, but still showing a strong curvature.

Electromagnetism

In classical electromagnetism, the vacuum of free space, or sometimes just free space or perfect vacuum, is a standard reference medium for electromagnetic effects. Some authors refer to this reference medium as classical vacuum, a terminology intended to separate this concept from QED vacuum or QCD vacuum, where vacuum fluctuations can produce transient virtual particle densities and a relative permittivity and relative permeability that are not identically unity.

In the theory of classical electromagnetism, free space has the following properties:

• Electromagnetic radiation travels, when unobstructed, at the speed of light, the defined value 299,792,458 m/s in SI units.
• The superposition principle is always exactly true. For example, the electric potential generated by two charges is the simple addition of the potentials generated by each charge in isolation. The value of the electric field at any point around these two charges is found by calculating the vector sum of the two electric fields from each of the charges acting alone.
• The permittivity and permeability are exactly the electric constant ε₀ and magnetic constant μ₀, respectively (in SI units), or exactly 1 (in Gaussian units).
• The characteristic impedance (η) equals the impedance of free space Z₀ ≈ 376.73 Ω.

The vacuum of classical electromagnetism can be viewed as an idealized electromagnetic medium with the constitutive relations in SI units:

${\displaystyle \mathit{D}(\mathit{r},t)={\epsilon }_0\mathit{E}(\mathit{r},t)}$

${\displaystyle \mathit{H}(\mathit{r},t)=\frac{1}{{\mu }_0}\mathit{B}(\mathit{r},t)}$

relating the electric displacement field D to the electric field E and the magnetic field or H-field H to the magnetic induction or B-field B. Here r is a spatial location and t is time.

Quantum mechanics

Main article: Quantum vacuum state

In quantum mechanics and quantum field theory, the vacuum is defined as the state (that is, the solution to the equations of the theory) with the lowest possible energy (the ground state of the Hilbert space). In quantum electrodynamics this vacuum is referred to as 'QED vacuum' to distinguish it from the vacuum of quantum chromodynamics, denoted as QCD vacuum. QED vacuum is a state with no matter particles (hence the name), and no photons. As described above, this state is impossible to achieve experimentally. (Even if every matter particle could somehow be removed from a volume, it would be impossible to eliminate all the blackbody photons.) Nonetheless, it provides a good model for realizable vacuum, and agrees with a number of experimental observations as described next.

QED vacuum has interesting and complex properties. In QED vacuum, the electric and magnetic fields have zero average values, but their variances are not zero. As a result, QED vacuum contains vacuum fluctuations (virtual particles that hop into and out of existence), and a finite energy called vacuum energy. Vacuum fluctuations are an essential and ubiquitous part of quantum field theory. Some experimentally verified effects of vacuum fluctuations include spontaneous emission and the Lamb shift. Coulomb's law and the electric potential in vacuum near an electric charge are modified.

Theoretically, in QCD multiple vacuum states can coexist. The starting and ending of cosmological inflation is thought to have arisen from transitions between different vacuum states. For theories obtained by quantization of a classical theory, each stationary point of the energy in the configuration space gives rise to a single vacuum. String theory is believed to have a huge number of vacua – the so-called string theory landscape.

Outer space

Main article: Outer space

Structure of the magnetosphere - is not a perfect vacuum, but a tenuous plasma awash with charged particles, free elements such as hydrogen, helium and oxygen, electromagnetic fields.

Outer space has very low density and pressure, and is the closest physical approximation of a perfect vacuum. But no vacuum is truly perfect, not even in interstellar space, where there are still a few hydrogen atoms per cubic meter.

Stars, planets, and moons keep their atmospheres by gravitational attraction, and as such, atmospheres have no clearly delineated boundary: the density of atmospheric gas simply decreases with distance from the object. The Earth's atmospheric pressure drops to about 32 millipascals (4.6×10⁻⁶ psi) at 100 kilometres (62 mi) of altitude, the Kármán line, which is a common definition of the boundary with outer space. Beyond this line, isotropic gas pressure rapidly becomes insignificant when compared to radiation pressure from the Sun and the dynamic pressure of the solar winds, so the definition of pressure becomes difficult to interpret. The thermosphere in this range has large gradients of pressure, temperature and composition, and varies greatly due to space weather. Astrophysicists prefer to use number density to describe these environments, in units of particles per cubic centimetre.

But although it meets the definition of outer space, the atmospheric density within the first few hundred kilometers above the Kármán line is still sufficient to produce significant drag on satellites. Most artificial satellites operate in this region, called low Earth orbit, and must fire their engines every couple of weeks or a few times a year (depending on solar activity). The drag here is low enough that it could theoretically be overcome by radiation pressure on solar sails, a proposed propulsion system for interplanetary travel.

All of the observable universe is filled with large numbers of photons, the so-called cosmic background radiation, and quite likely a correspondingly large number of neutrinos. The current temperature of this radiation is about 3 K (−270.15 °C; −454.27 °F).

Measurement

Main article: Pressure measurement

The quality of a vacuum is indicated by the amount of matter remaining in the system, so that a high quality vacuum is one with very little matter left in it. Vacuum is primarily measured by its absolute pressure, but a complete characterization requires further parameters, such as temperature and chemical composition. One of the most important parameters is the mean free path (MFP) of residual gases, which indicates the average distance that molecules will travel between collisions with each other. As the gas density decreases, the MFP increases, and when the MFP is longer than the chamber, pump, spacecraft, or other objects present, the continuum assumptions of fluid mechanics do not apply. This vacuum state is called high vacuum, and the study of fluid flows in this regime is called particle gas dynamics. The MFP of air at atmospheric pressure is very short, 70 nm, but at 100 mPa (≈10⁻³ Torr) the MFP of room temperature air is roughly 100 mm, which is on the order of everyday objects such as vacuum tubes. The Crookes radiometer turns when the MFP is larger than the size of the vanes.

Vacuum quality is subdivided into ranges according to the technology required to achieve it or measure it. These ranges were defined in ISO 3529-1:2019 as shown in the following table (100 Pa corresponds to 0.75 Torr; Torr is a non-SI unit):

Pressure range	Definition	The reasoning for the definition of the ranges is as follows (typical circumstances):
Prevailing atmospheric pressure (31 kPa to 110 kPa) to 100 Pa	low (rough) vacuum	Pressure can be achieved by simple materials (e.g. regular steel) and positive displacement vacuum pumps; viscous flow regime for gases
<100 Pa to 0.1 Pa	medium (fine) vacuum	Pressure can be achieved by elaborate materials (e.g. stainless steel) and positive displacement vacuum pumps; transitional flow regime for gases
<0.1 Pa to 1×10−6 Pa	high vacuum (HV)	Pressure can be achieved by elaborate materials (e.g. stainless steel), elastomer sealings and high vacuum pumps; molecular flow regime for gases
<1×10−6 Pa to 1×10−9 Pa	ultra-high vacuum (UHV)	Pressure can be achieved by elaborate materials (e.g. low-carbon stainless steel), metal sealings, special surface preparations and cleaning, bake-out and high vacuum pumps; molecular flow regime for gases
below 1×10−9 Pa	extreme-high vacuum (XHV)	Pressure can be achieved by sophisticated materials (e.g. vacuum fired low-carbon stainless steel, aluminium, copper-beryllium, titanium), metal sealings, special surface preparations and cleaning, bake-out and additional getter pumps; molecular flow regime for gases

• Atmospheric pressure is variable but 101.325 and 100 kilopascals (1013.25 and 1000.00 mbar) are common standard or reference pressures.
• Deep space is generally much more empty than any artificial vacuum. It may or may not meet the definition of high vacuum above, depending on what region of space and astronomical bodies are being considered. For example, the MFP of interplanetary space is smaller than the size of the Solar System, but larger than small planets and moons. As a result, solar winds exhibit continuum flow on the scale of the Solar System, but must be considered a bombardment of particles with respect to the Earth and Moon.
• Perfect vacuum is an ideal state of no particles at all. It cannot be achieved in a laboratory, although there may be small volumes which, for a brief moment, happen to have no particles of matter in them. Even if all particles of matter were removed, there would still be photons, as well as dark energy, virtual particles, and other aspects of the quantum vacuum.

Relative versus absolute measurement

Vacuum is measured in units of pressure, typically as a subtraction relative to ambient atmospheric pressure on Earth. But the amount of relative measurable vacuum varies with local conditions. On the surface of Venus, where ground-level atmospheric pressure is much higher than on Earth, much higher relative vacuum readings would be possible. On the surface of the Moon with almost no atmosphere, it would be extremely difficult to create a measurable vacuum relative to the local environment.

Similarly, much higher than normal relative vacuum readings are possible deep in the Earth's ocean. A submarine maintaining an internal pressure of 1 atmosphere submerged to a depth of 10 atmospheres (98 metres; a 9.8-metre column of seawater has the equivalent weight of 1 atm) is effectively a vacuum chamber keeping out the crushing exterior water pressures, though the 1 atm inside the submarine would not normally be considered a vacuum.

Therefore, to properly understand the following discussions of vacuum measurement, it is important that the reader assumes the relative measurements are being done on Earth at sea level, at exactly 1 atmosphere of ambient atmospheric pressure.

Measurements relative to 1 atm

A glass McLeod gauge, drained of mercury

The SI unit of pressure is the pascal (symbol Pa), but vacuum is often measured in torrs, named for an Italian physicist Torricelli (1608–1647). A torr is equal to the displacement of a millimeter of mercury (mmHg) in a manometer with 1 torr equaling 133.3223684 pascals above absolute zero pressure. Vacuum is often also measured on the barometric scale or as a percentage of atmospheric pressure in bars or atmospheres. Low vacuum is often measured in millimeters of mercury (mmHg) or pascals (Pa) below standard atmospheric pressure. "Below atmospheric" means that the absolute pressure is equal to the current atmospheric pressure.

In other words, most low vacuum gauges that read, for example 50.79 Torr. Many inexpensive low vacuum gauges have a margin of error and may report a vacuum of 0 Torr but in practice this generally requires a two-stage rotary vane or other medium type of vacuum pump to go much beyond (lower than) 1 torr.

Measuring instruments

Many devices are used to measure the pressure in a vacuum, depending on what range of vacuum is needed.

Hydrostatic gauges (such as the mercury column manometer) consist of a vertical column of liquid in a tube whose ends are exposed to different pressures. The column will rise or fall until its weight is in equilibrium with the pressure differential between the two ends of the tube. The simplest design is a closed-end U-shaped tube, one side of which is connected to the region of interest. Any fluid can be used, but mercury is preferred for its high density and low vapour pressure. Simple hydrostatic gauges can measure pressures ranging from 1 torr (100 Pa) to above atmospheric. An important variation is the McLeod gauge which isolates a known volume of vacuum and compresses it to multiply the height variation of the liquid column. The McLeod gauge can measure vacuums as high as 10⁻⁶ torr (0.1 mPa), which is the lowest direct measurement of pressure that is possible with current technology. Other vacuum gauges can measure lower pressures, but only indirectly by measurement of other pressure-controlled properties. These indirect measurements must be calibrated via a direct measurement, most commonly a McLeod gauge.

The kenotometer is a particular type of hydrostatic gauge, typically used in power plants using steam turbines. The kenotometer measures the vacuum in the steam space of the condenser, that is, the exhaust of the last stage of the turbine.

Mechanical or elastic gauges depend on a Bourdon tube, diaphragm, or capsule, usually made of metal, which will change shape in response to the pressure of the region in question. A variation on this idea is the capacitance manometer, in which the diaphragm makes up a part of a capacitor. A change in pressure leads to the flexure of the diaphragm, which results in a change in capacitance. These gauges are effective from 10³ torr to 10⁻⁴ torr, and beyond.

Thermal conductivity gauges rely on the fact that the ability of a gas to conduct heat decreases with pressure. In this type of gauge, a wire filament is heated by running current through it. A thermocouple or Resistance Temperature Detector (RTD) can then be used to measure the temperature of the filament. This temperature is dependent on the rate at which the filament loses heat to the surrounding gas, and therefore on the thermal conductivity. A common variant is the Pirani gauge which uses a single platinum filament as both the heated element and RTD. These gauges are accurate from 10 torr to 10⁻³ torr, but they are sensitive to the chemical composition of the gases being measured.

Ionization gauges are used in ultrahigh vacuum. They come in two types: hot cathode and cold cathode. In the hot cathode version an electrically heated filament produces an electron beam. The electrons travel through the gauge and ionize gas molecules around them. The resulting ions are collected at a negative electrode. The current depends on the number of ions, which depends on the pressure in the gauge. Hot cathode gauges are accurate from 10⁻³ torr to 10⁻¹⁰ torr. The principle behind cold cathode version is the same, except that electrons are produced in a discharge created by a high voltage electrical discharge. Cold cathode gauges are accurate from 10⁻² torr to 10⁻⁹ torr. Ionization gauge calibration is very sensitive to construction geometry, chemical composition of gases being measured, corrosion and surface deposits. Their calibration can be invalidated by activation at atmospheric pressure or low vacuum. The composition of gases at high vacuums will usually be unpredictable, so a mass spectrometer must be used in conjunction with the ionization gauge for accurate measurement.

Uses

Light bulbs contain a partial vacuum, usually backfilled with argon, which protects the tungsten filament

Vacuum is useful in a variety of processes and devices. Its first widespread use was in the incandescent light bulb to protect the filament from chemical degradation. The chemical inertness produced by a vacuum is also useful for electron-beam welding, cold welding, vacuum packing and vacuum frying. Ultra-high vacuum is used in the study of atomically clean substrates, as only a very good vacuum preserves atomic-scale clean surfaces for a reasonably long time (on the order of minutes to days). High to ultra-high vacuum removes the obstruction of air, allowing particle beams to deposit or remove materials without contamination. This is the principle behind chemical vapor deposition, physical vapor deposition, and dry etching which are essential to the fabrication of semiconductors and optical coatings, and to surface science. The reduction of convection provides the thermal insulation of thermos bottles. Deep vacuum lowers the boiling point of liquids and promotes low temperature outgassing which is used in freeze drying, adhesive preparation, distillation, metallurgy, and process purging. The electrical properties of vacuum make electron microscopes and vacuum tubes possible, including cathode-ray tubes. Vacuum interrupters are used in electrical switchgear. Vacuum arc processes are industrially important for production of certain grades of steel or high purity materials. The elimination of air friction is useful for flywheel energy storage and ultracentrifuges.

This shallow water well pump reduces atmospheric air pressure inside the pump chamber. Atmospheric pressure extends down into the well, and forces water up the pipe into the pump to balance the reduced pressure. Above-ground pump chambers are only effective to a depth of approximately 9 meters due to the water column weight balancing the atmospheric pressure.

Vacuum-driven machines

Vacuums are commonly used to produce suction, which has an even wider variety of applications. The Newcomen steam engine used vacuum instead of pressure to drive a piston. In the 19th century, vacuum was used for traction on Isambard Kingdom Brunel's experimental atmospheric railway. Vacuum brakes were once widely used on trains in the UK but, except on heritage railways, they have been replaced by air brakes.

Manifold vacuum can be used to drive accessories on automobiles. The best known application is the vacuum servo, used to provide power assistance for the brakes. Obsolete applications include vacuum-driven windscreen wipers and Autovac fuel pumps. Some aircraft instruments (Attitude Indicator (AI) and the Heading Indicator (HI)) are typically vacuum-powered, as protection against loss of all (electrically powered) instruments, since early aircraft often did not have electrical systems, and since there are two readily available sources of vacuum on a moving aircraft, the engine and an external venturi. Vacuum induction melting uses electromagnetic induction within a vacuum.

Maintaining a vacuum in the condenser is an important aspect of the efficient operation of steam turbines. A steam jet ejector or liquid ring vacuum pump is used for this purpose. The typical vacuum maintained in the condenser steam space at the exhaust of the turbine (also called condenser backpressure) is in the range 5 to 15 kPa (absolute), depending on the type of condenser and the ambient conditions.

Outgassing

Main article: Outgassing

Evaporation and sublimation into a vacuum is called outgassing. All materials, solid or liquid, have a small vapour pressure, and their outgassing becomes important when the vacuum pressure falls below this vapour pressure. Outgassing has the same effect as a leak and will limit the achievable vacuum. Outgassing products may condense on nearby colder surfaces, which can be troublesome if they obscure optical instruments or react with other materials. This is of great concern to space missions, where an obscured telescope or solar cell can ruin an expensive mission.

The most prevalent outgassing product in vacuum systems is water absorbed by chamber materials. It can be reduced by desiccating or baking the chamber, and removing absorbent materials. Outgassed water can condense in the oil of rotary vane pumps and reduce their net speed drastically if gas ballasting is not used. High vacuum systems must be clean and free of organic matter to minimize outgassing.

Ultra-high vacuum systems are usually baked, preferably under vacuum, to temporarily raise the vapour pressure of all outgassing materials and boil them off. Once the bulk of the outgassing materials are boiled off and evacuated, the system may be cooled to lower vapour pressures and minimize residual outgassing during actual operation. Some systems are cooled well below room temperature by liquid nitrogen to shut down residual outgassing and simultaneously cryopump the system.

Pumping and ambient air pressure

Deep wells have the pump chamber down in the well close to the water surface, or in the water. A "sucker rod" extends from the handle down the center of the pipe deep into the well to operate the plunger. The pump handle acts as a heavy counterweight against both the sucker rod weight and the weight of the water column standing on the upper plunger up to ground level.

Main article: Vacuum pump

Fluids cannot generally be pulled, so a vacuum cannot be created by suction. Suction can spread and dilute a vacuum by letting a higher pressure push fluids into it, but the vacuum has to be created first before suction can occur. The easiest way to create an artificial vacuum is to expand the volume of a container. For example, the diaphragm muscle expands the chest cavity, which causes the volume of the lungs to increase. This expansion reduces the pressure and creates a partial vacuum, which is soon filled by air pushed in by atmospheric pressure.

To continue evacuating a chamber indefinitely without requiring infinite growth, a compartment of the vacuum can be repeatedly closed off, exhausted, and expanded again. This is the principle behind positive displacement pumps, like the manual water pump for example. Inside the pump, a mechanism expands a small sealed cavity to create a vacuum. Because of the pressure differential, some fluid from the chamber (or the well, in our example) is pushed into the pump's small cavity. The pump's cavity is then sealed from the chamber, opened to the atmosphere, and squeezed back to a minute size.

A cutaway view of a turbomolecular pump, a momentum transfer pump used to achieve high vacuum

The above explanation is merely a simple introduction to vacuum pumping, and is not representative of the entire range of pumps in use. Many variations of the positive displacement pump have been developed, and many other pump designs rely on fundamentally different principles. Momentum transfer pumps, which bear some similarities to dynamic pumps used at higher pressures, can achieve much higher quality vacuums than positive displacement pumps. Entrapment pumps can capture gases in a solid or absorbed state, often with no moving parts, no seals and no vibration. None of these pumps are universal; each type has important performance limitations. They all share a difficulty in pumping low molecular weight gases, especially hydrogen, helium, and neon.

The lowest pressure that can be attained in a system is also dependent on many things other than the nature of the pumps. Multiple pumps may be connected in series, called stages, to achieve higher vacuums. The choice of seals, chamber geometry, materials, and pump-down procedures will all have an impact. Collectively, these are called vacuum technique. And sometimes, the final pressure is not the only relevant characteristic. Pumping systems differ in oil contamination, vibration, preferential pumping of certain gases, pump-down speeds, intermittent duty cycle, reliability, or tolerance to high leakage rates.

In ultra high vacuum systems, some very "odd" leakage paths and outgassing sources must be considered. The water absorption of aluminium and palladium becomes an unacceptable source of outgassing, and even the adsorptivity of hard metals such as stainless steel or titanium must be considered. Some oils and greases will boil off in extreme vacuums. The permeability of the metallic chamber walls may have to be considered, and the grain direction of the metallic flanges should be parallel to the flange face.

The lowest pressures currently achievable in laboratory are about 1×10⁻¹³ torrs (13 pPa). However, pressures as low as 5×10⁻¹⁷ torrs (6.7 fPa) have been indirectly measured in a 4 K (−269.15 °C; −452.47 °F) cryogenic vacuum system. This corresponds to ≈100 particles/cm³.

Effects on humans and animals

See also: Space exposure and Uncontrolled decompression

This painting, An Experiment on a Bird in the Air Pump by Joseph Wright of Derby, 1768, depicts an experiment performed by Robert Boyle in 1660.

Humans and animals exposed to vacuum will lose consciousness after a few seconds and die of hypoxia within minutes, but the symptoms are not nearly as graphic as commonly depicted in media and popular culture. The reduction in pressure lowers the temperature at which blood and other body fluids boil, but the elastic pressure of blood vessels ensures that this boiling point remains above the internal body temperature of 37 °C. Although the blood will not boil, the formation of gas bubbles in bodily fluids at reduced pressures, known as ebullism, is still a concern. The gas may bloat the body to twice its normal size and slow circulation, but tissues are elastic and porous enough to prevent rupture. Swelling and ebullism can be restrained by containment in a flight suit. Shuttle astronauts wore a fitted elastic garment called the Crew Altitude Protection Suit (CAPS) which prevents ebullism at pressures as low as 2 kPa (15 Torr). Rapid boiling will cool the skin and create frost, particularly in the mouth, but this is not a significant hazard.

Animal experiments show that rapid and complete recovery is normal for exposures shorter than 90 seconds, while longer full-body exposures are fatal and resuscitation has never been successful. A study by NASA on eight chimpanzees found all of them survived two and a half minute exposures to vacuum. There is only a limited amount of data available from human accidents, but it is consistent with animal data. Limbs may be exposed for much longer if breathing is not impaired. Robert Boyle was the first to show in 1660 that vacuum is lethal to small animals.

An experiment indicates that plants are able to survive in a low pressure environment (1.5 kPa) for about 30 minutes.

Cold or oxygen-rich atmospheres can sustain life at pressures much lower than atmospheric, as long as the density of oxygen is similar to that of standard sea-level atmosphere. The colder air temperatures found at altitudes of up to 3 km generally compensate for the lower pressures there. Above this altitude, oxygen enrichment is necessary to prevent altitude sickness in humans that did not undergo prior acclimatization, and spacesuits are necessary to prevent ebullism above 19 km. Most spacesuits use only 20 kPa (150 Torr) of pure oxygen. This pressure is high enough to prevent ebullism, but decompression sickness and gas embolisms can still occur if decompression rates are not managed.

Rapid decompression can be much more dangerous than vacuum exposure itself. Even if the victim does not hold his or her breath, venting through the windpipe may be too slow to prevent the fatal rupture of the delicate alveoli of the lungs. Eardrums and sinuses may be ruptured by rapid decompression, soft tissues may bruise and seep blood, and the stress of shock will accelerate oxygen consumption leading to hypoxia. Injuries caused by rapid decompression are called barotrauma. A pressure drop of 13 kPa (100 Torr), which produces no symptoms if it is gradual, may be fatal if it occurs suddenly.

Some extremophile microorganisms, such as tardigrades, can survive vacuum conditions for periods of days or weeks.